SOLUTION: The current river flows at the rate of 4mph. In order for a boat to travel 24 miles up river and then return I'm a total of 5 hours how fast must the boat be able to travel in stil

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Question 872087: The current river flows at the rate of 4mph. In order for a boat to travel 24 miles up river and then return I'm a total of 5 hours how fast must the boat be able to travel in still water?
Found 2 solutions by ankor@dixie-net.com, lwsshak3:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The current river flows at the rate of 4mph.
In order for a boat to travel 24 miles up river and then return in a total of 5 hours, how fast must the boat be able to travel in still water?
:
Let s = speed in still water
Then
(s-4) = effective speed upstream
and
(s+4) = effective speed downstream
:
Write a time equation, time = dist/speed
:
up-str time + down-str time = 5 hrs
24%2F%28%28s-4%29%29 + 24%2F%28%28s%2B4%29%29 = 5
Multiply by (s-4)(s+4)
(s-4)(s+4)*24%2F%28%28s-4%29%29 + (s-4)(s+4)24%2F%28%28s%2B4%29%29 = 5(s-4)(s+4)
Cancel the denominators, you have
24(s+4) + 24(s-4) = 5(s^2-16)
24s + 96 + 24s - 96 = 5s^2 - 80
48s = 5s^2 - 80
Combine to form a quadratic equation on the right
0 = 5s^2 - 48s - 80
This will not factor, use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+, where
x = s; a=5; b=-48; c=-80
x+=+%28-%28-48%29+%2B-+sqrt%28+-48%5E2-4%2A5%2A-80+%29%29%2F%282%2A5%29+
I'll let you do the math here, I got a positive solution of 11.05 mph
:
:
Check this in the original equation

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The current river flows at the rate of 4mph. In order for a boat to travel 24 miles up river and then return in a total of 5 hours how fast must the boat be able to travel in still water?
***
let x=speed of boat in still water
x+4=speed of boat downstream
x-4=speed of boat upstream
travel time=distance/speed
..
24/(x+4)+24/(x-4)=5
24(x-4)+24(x+4)=5(x+4)(x-4)
24x-96+24x+96=5(x^2-16)
48x=5x^2-80
5x^2-48x-80=0
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=5, b=-48, c=-80
ans:
x≈-1.45(reject)
or
x≈11.05
speed of boat in still water≈ 11.05 mph